DESCRIPTION

These macros define data structures for different types of trees: splay
trees and red-black trees.
In the macro definitions, TYPE is the name tag of a user defined
structure that must contain a field of type GG_SPLAY_ENTRY, or
GG_RB_ENTRY, named ENTRYNAME. The argument HEADNAME is the name tag of
a user defined structure that must be declared using the macros
GG_SPLAY_HEAD or GG_RB_HEAD. The argument NAME has to be a unique name
prefix for every tree that is defined.
The function prototypes are declared with either GG_SPLAY_PROTOTYPE or
GG_RB_PROTOTYPE. The function bodies are generated with either
GG_SPLAY_GENERATE or GG_RB_GENERATE. See the examples below for further
explanation of how these macros are used.

SPLAYTREES

A splay tree is a self-organizing data structure. Every operation on
the tree causes a splay to happen. The splay moves the requested node
to the root of the tree and partly rebalances it.
This has the benefit that request locality causes faster lookups as the
requested nodes move to the top of the tree. On the other hand, every
lookup causes memory writes.
The Balance Theorem bounds the total access time for m operations and n
inserts on an initially empty tree as O((m + n)lg n). The amortized
cost for a sequence of m accesses to a splay tree is O(lg n).
A splay tree is headed by a structure defined by the SPLAY_HEAD macro.
A GG_SPLAY_HEAD structure is declared as follows:
GG_SPLAY_HEAD(HEADNAME, TYPE) head;
where HEADNAME is the name of the structure to be defined, and struct
TYPE is the type of the elements to be inserted into the tree.
The GG_SPLAY_ENTRY macro declares a structure that allows elements to
be connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the GG_SPLAY_PROTOTYPE macro, where
NAME is a unique identifier for this particular tree. The TYPE
argument is the type of the structure that is being managed by the
tree. The FIELD argument is the name of the element defined by
GG_SPLAY_ENTRY.
The function bodies are generated with the GG_SPLAY_GENERATE macro. It
takes the same arguments as the GG_SPLAY_PROTOTYPE macro, but should be
used only once.
Finally, the CMP argument is the name of a function used to compare
trees noded with each other. The function takes two arguments of type
struct TYPE*. If the first argument is smaller than the second, the
function returns a value smaller than zero. If they are equal, the
function returns zero. Otherwise, it should return a value greater
than zero. The compare function defines the order of the tree
elements.
The GG_SPLAY_INIT macro initializes the tree referenced by head.
The splay tree can also be initialized statically by using the
GG_SPLAY_INITIALIZER macro like this:
GG_SPLAY_HEAD(HEADNAME, TYPE) head = GG_SPLAY_INITIALIZER(&head);
The GG_SPLAY_INSERT macro inserts the new element elm into the tree.
The GG_SPLAY_REMOVE macro removes the element elm from the tree pointed
by head.
The GG_SPLAY_FIND macro can be used to find a particular element in the
tree.:
struct TYPE find, *res;
find.key = 30;
res = GG_SPLAY_FIND(NAME, head, &find);
The GG_SPLAY_ROOT, GG_SPLAY_MIN, GG_SPLAY_MAX, and GG_SPLAY_NEXT macros
can be used to traverse the tree:
for (np = GG_SPLAY_MIN(NAME, &head); np != NULL; np = GG_SPLAY_NEXT(NAME, &head, np))
Or, for simplicity, one can use the GG_SPLAY_FOREACH macro:
GG_SPLAY_FOREACH(np, NAME, head)
The GG_SPLAY_EMPTY macro should be used to check whether a splay tree
is empty.

RED-BLACKTREES

A red-black tree is a binary search tree with the node color as an
extra attribute. It fulfills a set of conditions:
1 every search path from the root to a leaf consists of the same
number of black nodes,
2 each red node (except for the root) has a black parent,
3 each leaf node is black.
Every operation on a red-black tree is bounded as O(lg n). The maximum
height of a red-black tree is 2lg (n+1).
A red-black tree is headed by a structure defined by the GG_RB_HEAD
macro. A GG_RB_HEAD structure is declared as follows:
GG_RB_HEAD(HEADNAME, TYPE) head;
where HEADNAME is the name of the structure to be defined, and struct
TYPE is the type of the elements to be inserted into the tree.
The GG_RB_ENTRY macro declares a structure that allows elements to be
connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the GG_RB_PROTOTYPE macro, where
NAME is a unique identifier for this particular tree. The TYPE argument
is the type of the structure that is being managed by the tree. The
FIELD argument is the name of the element defined by GG_RB_ENTRY.
The function bodies are generated with the GG_RB_GENERATE macro. It
takes the same arguments as the GG_RB_PROTOTYPE macro, but should be
used only once.
Finally, the CMP argument is the name of a function used to compare
trees noded with each other. The function takes two arguments of type
struct TYPE*. If the first argument is smaller than the second, the
function returns a value smaller than zero. If they are equal, the
function returns zero. Otherwise, it should return a value greater
than zero. The compare function defines the order of the tree
elements.
The GG_RB_INIT macro initializes the tree referenced by head.
The redblack tree can also be initialized statically by using the
GG_RB_INITIALIZER macro like this:
GG_RB_HEAD(HEADNAME, TYPE) head = GG_RB_INITIALIZER(&head);
The GG_RB_INSERT macro inserts the new element elm into the tree.
The GG_RB_REMOVE macro removes the element elm from the tree pointed by
head.
The GG_RB_FIND macro can be used to find a particular element in the
tree.:
struct TYPE find, *res;
find.key = 30;
res = GG_RB_FIND(NAME, head, &find);
The GG_RB_ROOT, GG_RB_MIN, GG_RB_MAX, and GG_RB_NEXT macros can be used
to traverse the tree:
for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))
Or, for simplicity, one can use the RB_FOREACH macro:
GG_RB_FOREACH(np, NAME, head)
The GG_RB_EMPTY macro should be used to check whether a red-black tree
is empty.

NOTES

Trying to free a tree in the following way is a common error:
GG_SPLAY_FOREACH(var, NAME, head) {
GG_SPLAY_REMOVE(NAME, head, var);
free(var);
}
free(head);
Since var is free’d, the FOREACH macro refers to a pointer that may
have been reallocated already. Proper code needs a second variable.:
for (var = GG_SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
nxt = GG_SPLAY_NEXT(NAME, head, var);
GG_SPLAY_REMOVE(NAME, head, var);
free(var);
}
Both GG_RB_INSERT and GG_SPLAY_INSERT return NULL if the element was
inserted in the tree successfully, otherwise they return a pointer to
the element with the colliding key.
Accordingly, GG_RB_REMOVE and GG_SPLAY_REMOVE return the pointer to the
removed element, otherwise they return NULL to indicate an error.